Active vibration control of a nonlinear three-dimensional Euler–Bernoulli beam

In this paper, boundary control is designed to suppress the vibration of a nonlinear three-dimensional Euler–Bernoulli beam. Considering the coupling effect between the axial deformation and the transverse displacement, the dynamics of the beam are modeled as a distributed parameter system described...

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Bibliographic Details
Published in:Journal of vibration and control 2017-11, Vol.23 (19), p.3196-3215
Main Authors: He, Wei, Yang, Chuan, Zhu, Juxing, Liu, Jin-Kun, He, Xiuyu
Format: Article
Language:English
Subjects:
Active control
Adaptive control
Boundary control
Computer simulation
Deformation
Deformation effects
Differential equations
Euler-Bernoulli beams
Mathematical models
Nonlinear control
Ordinary differential equations
Partial differential equations
Vibration
Vibration control
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Summary:In this paper, boundary control is designed to suppress the vibration of a nonlinear three-dimensional Euler–Bernoulli beam. Considering the coupling effect between the axial deformation and the transverse displacement, the dynamics of the beam are modeled as a distributed parameter system described by three partial differential equations (PDEs) and 12 ordinary differential equations (ODEs). Firstly, model-based boundary control is designed based on a mathematical model of the system. Subsequently, adaptive control is proposed when there are parameter uncertainties in the model. The uniform boundedness and uniform ultimate boundedness are proved under the proposed control laws. Finally, numerical simulations illustrate the effectiveness of the results.
ISSN:1077-5463
1741-2986
DOI:10.1177/1077546315627722